In order to transmit data a carrier is modulated in accordance with a pre-established digital code. It is known to modulate the carrier using either amplitude, frequency or phase modulation. The time interval occupied by each modulation is known as the symbol (or digit) time interval.
In order to prevent energy appearing in the modulated signal over a wide range of frequencies the modulated signal is filtered. The act of filtering whilst attenuating energy appearing outside the passband of the filter causes the spreading in time of energy in one symbol into succeeding symbols. This effect is known as intersymbol interference (ISI).
Nyquist proposed a criteria for minimising the effects of ISI based upon the premise of confining each digit to its own time slot to as great an extent as possible, (Nyquist, H; "Certain Factors Affecting Telegraph Speed", Bell System Technical Journal; Vol 3, pp 324-326, April 1924).
The Nyquist criteria represent an ideal situation which cannot be met in practice, because it is not possible to have a precise relationship between the cut-off freuency of an ideal filter and the bit rate.
Partial-response techniques are known (Kretzmer, E. R., "Binary Data Communication by Partial-Response Transmission", Conference Record 1965, IEEE Annual Communications Conference, pp 451-455), and introduce deliberately, a limited amount of ISI over a span of one, two or more digits and capitalise on it. The net result is a spectral reshaping of binary or multi-level pulse trains.
The consequences are significant. For a given bandwidth, partial-response techniques permit the transmission of more bits per second per Hertz than Nyquist-type zero-memory systems for a specified probability-of-error criterion.
One form of partial response technique is the modified-duobinary which involves a correlation span of two digits. The frequency response H(f) of such a modified-duobinary filter is given by ##EQU1## where: f.sub.1 =1/2T, and
T is the symbol or digit time interval in seconds. PA1 H.sub.1 (f)=T sinc f.multidot.T where T is the symbol interval and PA1 H.sup..tau. (f) is a truncated version of a function H(f) whose time-domain response h(t) is given by ##EQU3## where f.sub.1 =1/2T, and the truncation is defined by ##EQU4##
Known methods of implementing a modified-duobinary filter are by passive filtering with phase equalization and by digital filtering.
There are now requirements to transmit data at high rates, e.g. upwards of 1.5 Mbps through band limited channels, such as microwave links. Both passive filters and digital filters are not able to operate satisfactorily at such high data rates. Also passive filters are generally very complex and expensive.